Skip to main content
SpringerLink
Log in

A Semigroup Formulation of a Nonlinear Size-Structured Distributed Rate Population Model

  • Conference paper
Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 118))

Abstract

A variation of the Sinko-Streifer model in population dynamics where besides the observable characteristics size in addition a non-observable characteristics responsible for variations in growth rates for individuals of the same size is investigated. It is shown that the model can be formulated as an abstract Cauchy problem in an appropriate Banach space. We proof wellposedness of the abstract linear problem and also for a nonlinear perturbation of the model.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. T. BANKS, L. W. BOTSFORD, F. KAPPEL, C. WANG, Modeling and estimation in size structured population models Math. Ecology, T. G. Hallam, L. J. Gross, S. A. Levin (Eds.), Singapore: World Scientific, 1988, pp. 521–541.

    Google Scholar 

  2. H. T. BANKS and B. G. FITZPATRICK, Estimation of growth rate distribution in size structure population models ,Quart. Appl. Math. 49 (1991), 215–235.

    MathSciNet  MATH  Google Scholar 

  3. H. T. BANKS and F. KAPPEL, Transformation semigroups and L1 -approximation for size structured population models ,Semigroup Forum 38 (1989), 141–155.

    Article  MathSciNet  MATH  Google Scholar 

  4. N. DUNFORD and J. T. SCHWARTZ, Linear Operators ,Wiley-Interscience, New York, 1971.

    MATH  Google Scholar 

  5. B. G. FITZPATRICK, Vector valued measure approach for a size structured population model ,J. Math. Anal. Appl.172 (1993), 73–91.

    Article  MathSciNet  MATH  Google Scholar 

  6. W. HUYER, A size structured population model with dispersion ,Institute für Mathematik Technische Universität Graz-Universität Graz Preprint No. 212–1992, May 1992; J. Math. Analysis Appl., to appear.

    Google Scholar 

  7. A. OKUBO, Diffusion and Ecological Problems: Mathematical Models ,Springer-Verlag, Berlin, 1980.

    MATH  Google Scholar 

  8. S. OHARU and T. TAKAHASHI, Locally Lipschiz continuous perterbations of linear dissipative operators and nonlinear semigroups ,Proceedings of the American Mathematical Society 100 (1987), 187–194.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. PAZY, Semigroups of Linear Operators and Applications to Partial Differential Equations ,Springer, New York, 1983.

    Book  MATH  Google Scholar 

  10. G. F. WEBB, Theory of nonlinear age-dependent population dynamics ,Marcel Dekker Inc., New York, 1985.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, 27695-8205, USA

    H. T. Banks

  2. Institut für Mathematik, Universität Graz, Heinrichstrasse 36, A8010, Graz, Austria

    F. Kappel

  3. Department of Mathematics, University of Southern California, Los Angeles, CA, 90089-1113, USA

    C. Wang

Authors
  1. H. T. Banks
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Kappel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Mathematik, Universitat Graz, Heinrichstrasse 36, A-8010, Graz, Austria

    W. Desch  & F. Kappel  & 

  2. Fachbereich Mathematik, Technische Universitat Berlin, Strasse des 17. Juni 136, D-10623, Berlin, Germany

    K. Kunisch

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Basel AG

About this paper

Cite this paper

Banks, H.T., Kappel, F., Wang, C. (1994). A Semigroup Formulation of a Nonlinear Size-Structured Distributed Rate Population Model. In: Desch, W., Kappel, F., Kunisch, K. (eds) Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena. ISNM International Series of Numerical Mathematics, vol 118. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8530-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8530-0_1

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9666-5

  • Online ISBN: 978-3-0348-8530-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation